I used my MTB through the snow and ice last winter on plain knoblies (not studded) and didn't have a single incident. As has been said, the issue isn't the freshly fallen snow but rather ice and compacted snow. On roads which get a medium amount of traffic and no grit, the snow can often turn into a slushy mess, which then freezes becoming rough with deep gullies where the tires of the cars have been.
When riding in the snow/ice it is important to not to accelerate or corner aggressively, and to make sure that you brake gently using the rear wheel. I don't advise using the front brake in the snow/ice as if it locks up you have a high chance of coming off! If I find myself on sheet ice with no studs, I just coast over it without changing direction or speed.
I've taken a look at your tires, and they seem to have a nice aggressive tread, which should be okay in the snow, however nothing but studs will get a good grip on ice.
This is my experience in snow riding, others may vary depending on location/snowfall etc.